This invention relates generally to reducing the corrosion potential of components exposed to high-temperature water through a noble metal application process. More specifically, the invention relates to a method and apparatus for modeling and maintaining the amount of noble metals deposited in the water circuit of a boiling water reactor and components thereof during an in situ noble metal application process.
Nuclear reactors are used in electric power generation, research and propulsion. A reactor pressure vessel contains the reactor coolant, i.e. water, which removes heat from the nuclear core. Respective piping circuits carry the heated water or steam to the steam generators or turbines and carry circulated water or feedwater back to the vessel. Operating pressures and temperatures for the reactor pressure vessel are about 7 MPa and 288EC for a boiling water reactor (BWR), and about 15 MPa and 320EC for a pressurized water reactor (PWR). The materials used in both BWRs and PWRs must withstand various loading, environmental and radiation conditions.
Some of the materials exposed to high-temperature water include carbon steel, alloy steel, stainless steel, nickel-based, cobalt-based and zirconium-based alloys. Despite careful selection and treatment of these materials for use in water reactors, corrosion occurs in the materials exposed to the high-temperature water. Such corrosion contributes to a variety of problems, e.g., stress corrosion cracking, crevice corrosion, erosion corrosion, sticking of pressure relief valves and buildup of the gamma radiation-emitting Co-60 isotope.
Stress corrosion cracking (SCC) is a known phenomenon occurring in reactor components, such as structural members, piping, fasteners and welds exposed to high-temperature water. As used herein, SCC refers to cracking propagated by static or dynamic tensile stressing in combination with corrosion at the crack tip. The reactor components are subject to a variety of stresses associated with, e.g., differences in thermal expansion, the operating pressure needed for the containment of the reactor cooling water, and other sources such as residual stress from welding, cold working and other asymmetric metal treatments. In addition, water chemistry, welding, heat treatment, and radiation can increase the susceptibility of metal in a component to SCC.
It is well known that SCC occurs at higher rates when oxygen is present in the reactor water in concentrations of about 5 ppb or greater. SCC is further increased in a high radiation flux where oxidizing species, such as oxygen, hydrogen peroxide, and short-lived radicals, are produced from radiolytic decomposition of the reactor water. Such oxidizing species increase the electrochemical corrosion potential (ECP) of metals. Electrochemical corrosion is caused by a flow of electrons from anodic to cathodic areas on metallic surfaces. The ECP is a measure of the thermodynamic tendency for corrosion phenomena to occur, and is a fundamental parameter in determining rates of, e.g., SCC, corrosion fatigue, corrosion film thickening, and general corrosion.
In a BWR, the radiolysis of the primary water coolant in the reactor core causes the net decomposition of a small fraction of the water to the chemical products H2, H2O2, O2 and oxidizing and reducing radicals. For steady-state operating conditions, equilibrium concentrations of O2, H2O2, and H2 are established in both the water which is recirculated and the steam going to the turbine. This concentration of O2, H2O2, and H2 is oxidizing and results in conditions that can promote intergranular stress corrosion cracking (IGSCC) of susceptible materials of construction. One method employed to mitigate IGSCC of susceptible material is the application of hydrogen water chemistry (HWC), whereby the oxidizing nature of the BWR environment is modified to a more reducing condition. This effect is achieved by adding hydrogen gas to the reactor feedwater. When the hydrogen reaches the reactor vessel, it reacts with the radiolytically formed oxidizing species to reform water, thereby lowering the concentration of dissolved oxidizing species in the water in the vicinity of metal surfaces. The rate of these recombination reactions is dependent on local radiation fields, water flow rates and other variables.
The injected hydrogen reduces the level of oxidizing species in the water, such as dissolved oxygen, and as a result lowers the ECP of metals in the water. However, factors such as variations in water flow rates and the time or intensity of exposure to neutron or gamma radiation result in the production of oxidizing species at different levels in different reactors. Thus, varying amounts of hydrogen have been required to reduce the level of oxidizing species sufficiently to maintain the ECP below a critical potential required for protection from IGSCC in high-temperature water. As used herein, the term xe2x80x9ccritical potentialxe2x80x9d means a corrosion potential at or below a range of values of about xe2x88x920.230 to xe2x88x920.300 V based on the standard hydrogen electrode (SHE) scale. IGSCC proceeds at an accelerated rate in systems in which the ECP is above the critical potential, and at a substantially lower or zero rate in systems in which the ECP is below the critical potential. Water containing oxidizing species such as oxygen increases the ECP of metals exposed to the water above the critical potential, whereas water with little or no oxidizing species presents results in an ECP below the critical potential.
Corrosion potentials of stainless steels in contact with reactor water containing oxidizing species can be reduced below the critical potential by injection of hydrogen into the water so that the dissolved hydrogen concentration is about 50 to 100 ppb or greater. For adequate feedwater hydrogen addition rates, conditions necessary to inhibit IGSCC can be established in certain locations of the reactor. Different locations in the reactor system require different levels of hydrogen addition. For example, much higher hydrogen injection levels are necessary to reduce the ECP within the high radiation flux of the reactor core, or when oxidizing cationic impurities, e.g., cupric ion, are present.
An effective step toward to achieving the goal of reducing ECP within the high radiation flux of the reactor core is to either coat or alloy the stainless steel surface with palladium or any other noble group metal. As used herein, the term xe2x80x9cnoble metalxe2x80x9d means metals from the group consisting of platinum, palladium, osmium, ruthenium, iridium, rhodium, and mixtures thereof. The presence of palladium or other noble metal on the stainless steel surface catalyzes the recombination of oxidizing and reducing species in contact with the surface and reduces the injected hydrogen demand in achieving the required IGSCC critical potential of xe2x88x920.230 V(SHE). Known techniques for palladium coating include electroplating, electroless plating, plasma deposition and related high-vacuum techniques. Palladium alloying can also be carried out using standard alloy preparation techniques. Unfortunately, both of these approaches are ex situ techniques in that they cannot be practiced while the reactor is in operation.
U.S. Pat. No. 5,135,709 to Andresen et al. discloses a method for lowering the ECP on components formed from carbon steel, alloy steel, stainless steel, nickel-based alloys or cobalt-based alloys which are exposed to high-temperature water by forming the component to have a catalytic layer of a platinum group metal. As used therein, the term xe2x80x9ccatalytic layerxe2x80x9d means a coating on a substrate, or a solute in an alloy formed into the substrate, the coating or solute being sufficient to catalyze the recombination of oxidizing and reducing species at the surface of the substrate.
In nuclear reactors, ECP is increased by the high levels of oxidizing species, e.g., up to 200 ppb or greater of oxygen in the water measured in the circulation piping, produced from the radiolytic decomposition of water in the core of the nuclear reactor. The method disclosed in U.S. Pat. No. 5,135,709 further comprises providing a reducing species in the high-temperature water that can combine with the oxidizing species. In accordance with this known method, high concentrations of hydrogen, i.e., about 100 ppb or more, must be added to the water to provide adequate protection to materials outside the reactor core region, and still higher concentrations are needed to afford protection to materials in the reactor core.
The formation of a catalytic layer of a platinum group metal on an alloy from the aforementioned group catalyzes the recombination of reducing species, such as hydrogen, with oxidizing species, such as oxygen or hydrogen peroxide, that are present in the water of a BWR. Such catalytic action at the surface of the alloy can lower the ECP of the alloy below the critical potential where IGSCC is minimized. As a result, the efficacy of hydrogen additions to high-temperature water in lowering the ECP of components made from the alloy and exposed to the injected water is increased many-fold. Furthermore, it is possible to provide catalytic activity at metal alloy surfaces if the metal substrate of such surfaces contains a catalytic layer of a platinum group metal. Relatively small amounts of the platinum group metal are sufficient to provide the catalytic layer and catalytic activity at the surface of the metal substrate.
Thus, lower amounts of reducing species such as hydrogen are effective in reducing the ECP of the metal components below the critical potential, because the efficiency of recombination of oxidizing and reducing species is increased many-fold by the catalytic layer. Reducing species that can combine with the oxidizing species in the high-temperature water are provided by conventional means known in the art. In particular, reducing species such as hydrogen, ammonia, or hydrazine are injected into the feedwater of the nuclear reactor. However, a need still exists to provide for improved control over the deposition of platinum, palladium or other catalytic metals onto the surface of components in situ. The present invention seeks to satisfy that need.
In this regard, it has been discovered that it is possible to control the amount of metal species deposited on metal surfaces by carefully controlling the water temperature into which the metal is introduced within a particular temperature range. It has also been discovered, that by careful selection of the water temperature, metal concentration and time, it is possible to control the deposit ratio of a particular metal from a mixture of metals.
In addition, it has been found that an unexpectedly increased loading of the deposited metal occurs when the temperature of the water is selected to be within the range of about 200xc2x0 F. to 550xc2x0 F., more particularly within the range of about 300xc2x0 F. to about 450xc2x0 F., as compared to the loading obtained at temperatures above or below that range. This allows for the selection of a particular metal loading on the metal surface by a careful selection of the appropriate water temperature into which the compound containing the metal species to be deposited is introduced. The deposited metal is typically a noble metal and is introduced in the absence of hydrogen or other added reducing agents.
Moreover, the above described process may be carried out in the presence of hydrogen and other reducing agents. For example, commonly assigned with the present invention, U.S. Pat. Nos. 5,600,691 and 5,818,893 teach an in situ noble metal application process, forming the basis of what is generically referred to herein as the NobleChem(trademark) process, whereby palladium or other catalytic metals are deposited onto stainless steel or other metal surfaces immersed in high-temperature water such that the catalytic metal penetrates into existing cracks in the metal surfaces. During this NobleChem(trademark) process, noble or other catalytic metals are added to the water coolant in the reactor core as a metal-containing compound that is introduced in an amount such that, upon decomposition of the metal-containing compound in the water, the metal atoms are released in an amount sufficient, when present on the metal surface, to reduce the electrochemical corrosion potential of the metal to a level below the critical potential, and thereby protect against intergranular stress corrosion cracking.
Basically, the NobleChem(trademark) process provides a method for reducing corrosion of alloy components such as stainless steel components, in a water-cooled nuclear reactor or associated components, wherein a solution of a compound containing a noble metal (or other catalytic metals) is injected into the reactor water at a temperature of about to 200xc2x0 to 550xc2x0 F., for example about 300xc2x0 to 450xc2x0 F., in an amount such that, upon decomposition of the compound under the operating reactor thermal conditions, atoms of the metal compound are released at a rate such that the concentration of the metal in the water is sufficient, once incorporated on the alloy components, to reduce the electrochemical corrosion potential of the alloy components to a level below the critical potential. Hydrogen may be present at low levels, for example, preferably less than 400 ppb but acceptably about 300-600 ppb. In this way, the alloy reactor components are protected against intergranular stress corrosion cracking.
The above described NobleChem(trademark) process is based on the discovery that it is possible to control the amount of metals deposited on an oxidized metal surface in high temperature water, as well as the ratio of metal deposit from a mixture of metals, by careful choice of the temperature of the water, concentration of the metal and time. Generally, the preferred noble metals used for the NobleChem(trademark) process are incorporated into a compound containing platinum and rhodium. For example, with a platinum/rhodium mixture, the weight ratio within the temperature range of 200xc2x0 F.-550xc2x0 F. is typically from about 5:1 to about 40:1 platinum:rhodium. The compound has the property that it decomposes in the high-temperature water to release atoms of the metal which incorporate in the oxide film at a particular loading level.
Compounds of the platinum group metals are preferred. The term xe2x80x9ca platinum group metalxe2x80x9d, as used herein, means platinum, palladium, osmium, ruthenium, iridium, rhodium and mixtures thereof. It is also possible to use compounds of non-platinum group metals, such as for example zinc, titanium, zirconium, niobium, tantalum, tungsten and vanadium. Mixtures of platinum group compounds may also be used. Mixtures of platinum group compounds and non-platinum group compounds may also be used in combination, for example platinum and zinc. The compounds may be organo-metallic, organic or inorganic and may be soluble or insoluble in water (i.e. may form solutions or suspensions in water and/or other media such alcohols and/or acids). Generally, when mixtures of platinum and non-platinum group metals are used, the platinum group metal is in excess of the other metal.
Examples of preferred platinum group metal compounds which may be used and examples of mixtures of the compounds which may be used are discussed in greater detail in the above mentioned patents. Use of such mixtures results in the incorporation of various noble metals in the oxidized stainless steel surfaces within the reactor.
The noble metal-containing compound is injected in situ into the high-temperature water of a BWR (or PWR) in an amount such as to produce, upon decomposition of the compound, a metal concentration of up to 2000 ppb, for example about 1 to 850 ppb, more usually 5 to 100 ppb. The high temperatures as well as the gamma and neutron radiation in the reactor core act to decompose the compound, thereby freeing noble metal ions/atoms for deposition on the surface of the oxide film. (As used herein, the term xe2x80x9catomsxe2x80x9d means atoms or ions).
The noble metal injection solution may be prepared for example by dissolving the noble metal compound in ethanol. The ethanol solution is then diluted with water. Alternatively, a water-based suspension can be formed, without using ethanol, by mixing the noble metal compound in water.
The noble metal either deposits or is incorporated into the stainless steel oxide film via a thermal decomposition process of the noble metal compound. As a result of that decomposition, noble metal ions/atoms become available to replace atoms, e.g., iron atoms, in the oxide film, thereby producing a noble metal-doped oxide film on stainless steel.
The noble metal-containing compound may be injected directly into the water of the reactor in situ in the form of an aqueous solution or suspension, or may be dissolved in the water before it is introduced to the reactor. For the sake of this discussion, the term xe2x80x9csolutionxe2x80x9d means solution or suspension. Such solutions and suspensions may be formed using media well known to those skilled in the art. Examples of suitable media in which solutions and/or suspensions are formed, are water, alkanols such as ethanol, propanol, n-butanol, and acids such as lower carboxylic acids, e.g. acetic acid, propionic acid and butyric acid.
U.S. Pat. No. 5,818,893, entitled xe2x80x9cIn-Situ Palladium Doping Or Coating Of Stainless Steel Surfacesxe2x80x9d, which is commonly assigned with the present invention and incorporated herein by reference, discusses the effect of variation of temperature on metal deposit loading rate in greater detail, as well as the effect of distance from the point of introduction of the compound to the region of deposit on the metal surface. As demonstrated in that patent, an enhanced loading is observed over the temperature range of 200xc2x0 to 500xc2x0 F., more especially in the range of 300xc2x0 to 450xc2x0 F., and particularly at about 340xc2x0 to 360xc2x0 F. The loading observed in the temperature range of 300 to 450xc2x0 F. extends from about 10 xcexcg/cm2 at about 300xc2x0 F. to a maximum of about 62 xcexcg/cm2 at about 340xc2x0 F., and then drops off to about 10 xcexcg/cm2 and lower as the temperature rises towards 500xc2x0 F. This peaking effect is surprising and affords the advantage that loading of the metal species on the metal surface can be controlled by careful selection of the water temperature and point of introduction of the metal to be deposited.
When the metal compound solution or suspension enters the high-temperature water, the compound decomposes very rapidly to produce atoms, which are incorporated into the metal (typically stainless steel) oxide film. In accordance with the above described process, only the solution or suspension of the compound is introduced into the high-temperature water initially. No further agents, such as hydrogen, other reducing agents, acids or bases are introduced into the high-temperature water when the compound solution or suspension is injected into and decomposes in the high-temperature water.
The presence of rhodium renders the deposit more durable. However, it was found that as the temperature of water in the reactor reaches 300xc2x0 to 500xc2x0 F., the ratio of deposited platinum to rhodium drops to within the range of about 5:1 to 10:1. Thus, knowing this relationship, it is possible to control the ratio of platinum to rhodium in the deposited layer based on the prevailing temperature conditions of the water. In addition, the deposition rate for a 60 ppb platinum and 20 ppb rhodium solution is a negative exponential with temperature in the 180 to 350xc2x0 F. range. Thus, it is possible to predict the effect of temperature on the ratio of deposit of the metals and the time required to deposit a given quantity of noble metal in the oxide. Accordingly, the bulk concentration of platinum and rhodium, time and temperature are all controllable variables that may be used to produce a desired platinum-to-rhodium deposit ratio and a desired total noble metal loading.
The noble metal-containing compound solution or suspension may be injected into the high-temperature water while the reactor is operating and generating nuclear heat (full power operation), or during cool down, during outage, during heat-up, during hot standby, or during low power operation. Preferably, the noble metal is introduced into residual heat removal (RHR) piping, recirculation piping, feedwater line, core delta P line, jet pump instrumentation line, control rod drive cooling water lines, water level control points, or any other location which provides introduction of the noble metal into the reactor water and good mixing with the water. As used herein, the term xe2x80x9chigh-temperature waterxe2x80x9d in the present invention means water having a temperature of about 200xc2x0 F. or greater, steam, or the condensate thereof. High temperature water can be found in a variety of known apparatus, such as water deaerators, nuclear reactors, and steam-driven power plants. The temperature of the water when noble metal is added to the reactor water is typically in the range of 200-500xc2x0 F., for example 200-450xc2x0 F., more usually about 340xc2x0-360xc2x0 F. When the noble metal-containing compound is in the high-temperature water, it decomposes very rapidly and the metal atoms are incorporated in the oxide surface.
Preferably, only very dilute compound solution or suspension is injected into the high-temperature water. No reducing agents (including hydrogen), acids and bases, are added. As a result, the typical pH of the water at ambient temperature is in the region of 6.5 to 7.5, and at higher operating temperatures is lower, generally in the region of about 5.5-5.8, for example 5.65. (This is due to increased dissociation of the water at the higher temperatures.) In addition, an operating BWR has very stringent coolant water conductivity levels which must be observed. Typically, the conductivity of the coolant water must not exceed 0.3 FS/cm, and more usually must be less than 0.1 FS/cm. Such conductivity levels are adversely impacted by high concentrations of ionic species, and effort is made in the NobleChem(trademark) to ensure that reactor ionic concentrations are maintained as low as possible after clean-up, preferably less than 5 ppb. For example, the process in particular excludes the use of chloride ion in view of its corrosive nature.
While not being bound by theory, it is understood that the metal, for example platinum and/rhodium, is incorporated into the stainless steel oxide film via a thermal decomposition process of the compound wherein metal ions/atoms apparently replace iron, nickel and/or chromium atoms in the oxide film, resulting in a metal-doped oxide film. The metal, such as platinum/rhodium, may for example be incorporated within or on the surface of the oxide film and may be in the form of a finely divided metal. The oxide film is believed to include mixed nickel, iron and chromium oxides.
Following injection and incorporation of the metal(s) in the oxidized stainless steel surfaces, the water is subjected to a conventional clean-up process to remove ionic materials such as nitrate ions present in the water. This clean-up process is usually carried out by passing a fraction of the water removed from the bottom head of the reactor and recirculation piping through an ion exchange resin bed, and the treated water is then returned to the reactor via the feedwater system. Hydrogen may subsequently be introduced into the water some time after the doping reaction, for example 1 to 72 hours after injection and incorporation of the metal atoms in the oxidized surface, to catalyze recombination of hydrogen and oxygen on the metal doped surfaces. As hydrogen is added, the potential of the metal-doped oxide film on the stainless steel components is reduced to values which are, much more negative than when hydrogen is injected into a BWR having stainless steel components which are not doped with the noble metal.
The NobleChem(trademark) process, as basically and briefly outlined above, offers the advantage that steel surfaces within a water-cooled reactor can be doped with noble metal using an in situ technique (i.e., while the reactor is operating) that is simple in application and also inexpensive. Moreover, the process can also be applied to both operating BWRs and PWRs. However, during the NobleChem(trademark) process or any similar in situ metal deposition process, it is necessary to make certain informed decisions concerning how and when to modify various reactor operating conditionsxe2x80x94such as water temperature and noble metal-containing compound injection ratexe2x80x94to maintain proper metal loading throughout the deposition process.
Conventionally, the only way to obtain information on the state of a dynamic fluid system has been to perform simple non-steady state mass balances on the fluid within the system. Unfortunately, the procuring of a simple mass balance has proved inadequate for accurately assessing the state of metal deposition and controlling metal loading during in situ reactor deposition processes such as the above described NobleChem(trademark) processxe2x80x94due at least in part to the non-uniformity of metal deposition that typically occurs throughout the water flow circuit in a reactor in addition to other logistical factors inherent to the in situ process and environment as a whole.
The present invention relates to both a method and system for modeling and maintaining the amount of noble metals deposited in the water flow circuit of a boiling water reactor during an in situ noble metal application process, such as the NobleChem(trademark) process described above. A non-steady state computer model of the water in a Boiling Water Reactor (BWR) primary water flow circuit, and other piping directly connected to it, is used to represent the water chemistry and the noble metal loading that occurs before, during and after the noble metal application process. The modeling program tracks the noble metal application process via computed simulation based on reactor conditions and water samples (also called xe2x80x9ccouponsxe2x80x9d) taken, for example, at various locations throughout the flow circuit every few hours or so. Such testing of the flow circuit water may be performed during the metal application process while the reactor is operating, for example, in a xe2x80x9chot standbyxe2x80x9d mode.
In an example embodiment of the present invention, a software system for modeling water in a BWR is provided as an application/utility for use on a computer system having an associated display device and/or other output device for producing graphs and charts (e.g., a PDA, laptop, etc.). The software program code for the noble metal deposition modeling method of the present invention may be embodied in any computer-readable medium for loading and executing on a computer system. Preferably, the modeling software of the present invention is provided on a laptop or portable computer to enhance its transportability for use at different reactor sites. An Exel(trademark) spreadsheet program is used to create a workbook of spreadsheets containing power plant system data for modeling reactor water circuit flow that include geometric configuration data, pertinent operational parameters, simulation parameters, chemical parameters and initial water chemistry data. Alternatively, a portable electronic digital communications device having access via a wireless or landline digital communications link such as, for example, the Internet to a remote computer that performs the noble metal deposition modeling as described herein is also contemplated by the present invention.
The following description is directed toward a presently preferred embodiment of the present invention, which may be operative as an end-user application running, for example, under the Microsoft(copyright) Windows 95/NT environment. The present invention, however, is not limited to any particular computer system or any particular environment. Instead, those skilled in the art will find that the system and methods of the present invention may be implemented using almost any contemporary conventional personal or desktop computer system or computer network. Moreover, the invention may be embodied on a variety of different platforms, including UNIX, LINUX, Macintosh, Next Step, Open VMS, and the like. Therefore, the description of the exemplary embodiments which follows is for purposes of illustration and not limitation.
Information and system data characterizing a particular reactor plant may be placed, for example, on a magnetic disk (or other portable storage device) in the form of comma delimited text files. After the data representing the initial state of the reactor water chemistry and initial operating conditions of the reactor is read and input into the appropriate spreadsheet file, the modeling software determines the water chemistry, pH, conductivity and noble metal loading through the BWR primary water flow circuit, including selected sampling locations, as a function of time. The results are saved in files and displayed as charts or graphs for ascertaining whether technical specifications on conductivity or other water chemistry-related parameters will be exceeded during the noble metal application process.
In addition, the values of rate constants used for modeling the noble metal reactions can be changed on site at the reactor during an ongoing in situ application process and the modeling routine re-run until the numerical results from the computer model become consistent with actual measured concentrations of noble metals at selected sample locations. In this manner, a xe2x80x9cbest estimatexe2x80x9d of the noble metal loading occurring within the BWR water flow circuit is obtained and the operating conditions of the reactor can then be immediately changed if the calculated loading rates are inconsistent with predetermined target goals.
In an example embodiment of the metal deposition process modeling aspect of the present invention, each region of the reactor water flow circuit is characterized as being comprised of smaller xe2x80x9ccellsxe2x80x9d of equal flow residence time. In this manner, non-steady state mass balances can be maintained where parallel flow regions merge despite unequal flow residence times in each region. Mass balances are performed on all cells to account for transport-in, transport-out and chemical reactions. The concentrations of all relevant ionic species (including Clxe2x88x92, Na+, NO2xe2x88x92, NO3xe2x88x92, SO4xe2x88x92, ZnOH, Pt(OH)6xe2x88x92xe2x88x92, Rh(NO2)6xe2x88x92xe2x88x92xe2x88x92, OHxe2x88x92, H+) are determined based upon the initial concentrations in the flow circuit, measured concentrations in inlet and outlet streams, reactor water clean-up efficiency and local reaction rates. The cumulative concentrations of all the ionic species are then used to determine pH and conductivity. Reaction rates are also determined both for bulk processes (such as the decomposition of noble metal complexes due to thermal decomposition, radiation and other chemicals) and the reactions of chemical species with the metal surfaces in the flow circuit, including the deposition of noble metal with the simultaneous formation of OHxe2x88x92 or NO2xe2x88x92. These surface reaction rates are used for determining noble metal accumulation rates and consequent accumulated noble metal concentrations on the surfaces throughout the circuit.
In the disclosed example embodiment, the noble metal application process modeling routine of the present invention is complemented with conventional macro routines for generating and displaying prescribed graphs from initial data and for importing new data developed from each xe2x80x9crunxe2x80x9d (i.e., execution of the process modeling software) so that selected graphs may be re-plotted as desired. For example, a macro routine is provided for importing data from a modeling run into an Excel(trademark) workbook containing forms for generating prescribed graphs of interest. Likewise, another macro routine is provided for linking an Excel(trademark) workbook containing a graph to a previously generated set of graphs.
The modeling method of the present invention is also useful in performing non-steady state evaluations of water chemistry transients in BWRs. For example, concentrations of water impurities in a BWR due to leaking fuel rods, corroding components or other intrusions can be easily modeled by including xe2x80x9csourcexe2x80x9d terms in the modeling routine to represent an impurities at probable locations that might account for their appearance. Likewise, the disappearance of various impurities, for example, due to incorporation into crud or radioactive decay, can be accounted for by including representative xe2x80x9csinkxe2x80x9d terms in the modeling routine. In this manner, the non-steady state concentration of radioactive isotopes, corrosion products and water impurities could be determined for the entire water flow circuit(s) throughout the reactor and in the steam for performing, for example, analysis on fuel leaks and corrosion.